Last updated: November 19, 2025
Pythagorean theorem calculator explained
Right triangles obey , where is the hypotenuse. This calculator rearranges that relationship to solve for any missing leg or the hypotenuse, with unit conversions for metric or imperial measurements.
How the conversion works
Given two sides of a right triangle:
The tool enforces and ensures the square-root arguments stay positive.
Units and conversions
| Quantity | Units | Notes |
|---|---|---|
| Legs , | mm, cm, m, in, ft, yd | Converted to meters internally before squaring. |
| Hypotenuse | same | Output uses the unit selected for inputs. |
Worked examples
- Classic 3-4-5 triangle
, :
- Solve for a leg
, .
Tips and pitfalls
- The theorem only applies to right triangles; verify the angle is 90^\\circ before using it.
- Convert mixed units (e.g., feet and inches) to a single unit prior to calculation.
- In coordinate geometry, use the theorem to measure distances: .
- The squared relationship magnifies measurement errors, so measure carefully for large structures.